There isn't a solid answer to your question.

Why? Because while many believe that the US had a sort of open door to immigration until the late 19thC, the US has always been the product of immigration policy. Colonies had their own policies, and the British Crown certainly arranged immigration to those colonies in order to develop and exploit resources. Desirable groups were allowed and encouraged to immigrate. Undesirable groups were shown the door.

Heck, Jefferson included this in the Declaration of Independence: "He has endeavoured to prevent the population of these States; for that purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their migrations hither, and raising the conditions of new Appropriations of Lands."

There isn't a graph-able timeline of immigration policy where immigrants are allowed or blocked. It is an enormously complex interweaving of economics, politics, identity, and power. Far too complex to give you a simple answer.

If this is something in which you have a genuine interest, pick up Aristide Zolberg's A Nation by Design. It's a big book -- in both size and importance -- but it's quite readable and does a fantastic job of unpacking most of the complexities involved.